Subgroups — C₆₁×#24972 #29528405

Order 15616.

770 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2538	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2354	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2077	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2035	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1954	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1873	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1825	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₆₁	C₂²	1	2	yes	—
16	C₂×#106×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#103×C₆₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#396	—	2	2	no	—
25	C₆₁×#390	—	2	1	no	—
26	C₆₁×#390	—	2	1	no	—
27	C₆₁×#389	—	2	1	no	—
28	C₆₁×#388	—	2	2	no	—
29	C₆₁×#384	C₂²	1	1	yes	characteristic
30	C₆₁×#384	C₂²	1	1	yes	characteristic
31	C₆₁×#380	C₂²	1	2	yes	—
32	C₆₁×#380	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
34	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#340	C₂²	1	1	yes	characteristic
36	C₆₁×#340	C₂²	1	1	yes	characteristic
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
47	C₂²⋊Q₈×C₆₁	—	2	4	no	—
48	C₂²⋊Q₈×C₆₁	—	4	2	no	—
49	C₄×Q₈×C₆₁	—	2	2	no	—
50	C₄×Q₈×C₆₁	—	2	2	no	—
51	C₄×D₄×C₆₁	—	2	2	no	—
52	C₄×D₄×C₆₁	—	2	2	no	—
53	#117×C₆₁	—	2	4	no	—
54	#117×C₆₁	—	4	2	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
72	C₂×C₄²×C₆₁	—	2	1	no	—
73	C₂×C₄²×C₆₁	—	2	2	no	—
74	C₂×C₄²×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	#106×C₆₁	—	4	2	no	—
77	C₄⋊C₈×C₆₁	—	2	2	no	—
78	#103×C₆₁	—	2	2	no	—
79	#103×C₆₁	—	2	2	no	—
80	#103×C₆₁	—	4	2	no	—
81	C₂²⋊C₈×C₆₁	—	4	2	no	—
82	C₂²⋊C₈×C₆₁	—	4	2	no	—
83	C₄×C₈×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	1	no	—
86	#95×C₆₁	—	2	2	no	—
87	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
88	C₂×Q₈×C₆₁	—	2	1	no	—
89	C₂×Q₈×C₆₁	—	2	1	no	—
90	C₂×Q₈×C₆₁	—	2	1	no	—
91	C₂×Q₈×C₆₁	—	2	1	no	—
92	C₂×Q₈×C₆₁	—	2	1	no	—
93	C₂×Q₈×C₆₁	#41	1	2	yes	—
94	C₂×D₄×C₆₁	—	2	2	no	—
95	C₂×D₄×C₆₁	—	2	2	no	—
96	C₂×D₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	—	2	1	no	—
99	C₂²×C₄×C₆₁	—	2	2	no	—
100	C₂²×C₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₆₁	—	2	1	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	2	1	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	1	no	—
124	C₄⋊C₄×C₆₁	—	2	1	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	1	no	—
127	C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	4	4	no	—
133	C₄⋊C₄×C₆₁	—	4	2	no	—
134	C₄⋊C₄×C₆₁	—	4	2	no	—
135	C₄⋊C₄×C₆₁	—	4	2	no	—
136	C₄⋊C₄×C₆₁	—	8	1	no	—
137	C₄⋊C₄×C₆₁	—	8	1	no	—
138	C₄⋊C₄×C₆₁	#41	1	2	yes	—
139	C₂²⋊C₄×C₆₁	—	2	4	no	—
140	C₂²⋊C₄×C₆₁	—	4	4	no	—
141	C₂²⋊C₄×C₆₁	—	4	4	no	—
142	C₂²⋊C₄×C₆₁	—	8	2	no	—
143	C₂²⋊C₄×C₆₁	—	8	2	no	—
144	C₄²×C₆₁	—	4	4	no	—
145	C₄²×C₆₁	—	4	2	no	—
146	C₄²×C₆₁	—	4	2	no	—
147	C₄²×C₆₁	#41	1	2	yes	—
148	C₄²×C₆₁	#41	1	2	yes	—
149	C₂³×C₆₁	—	2	2	no	—
150	C₂³×C₆₁	—	2	2	no	—
151	C₂³×C₆₁	—	2	2	no	—
152	C₂³×C₆₁	—	2	2	no	—
153	C₂³×C₆₁	—	2	2	no	—
154	C₂³×C₆₁	—	2	2	no	—
155	C₂³×C₆₁	—	2	2	no	—
156	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₆₁	—	2	2	no	—
158	Q₈×C₆₁	—	2	2	no	—
159	Q₈×C₆₁	—	4	1	no	—
160	Q₈×C₆₁	—	4	1	no	—
161	D₄×C₆₁	—	4	4	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	2	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	4	1	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	1	no	—
172	C₂×C₄×C₆₁	—	4	1	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	1	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	1	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	1	no	—
184	C₂×C₄×C₆₁	—	4	1	no	—
185	C₂×C₄×C₆₁	—	4	1	no	—
186	C₂×C₄×C₆₁	—	4	2	no	—
187	C₂×C₄×C₆₁	—	4	2	no	—
188	C₂×C₄×C₆₁	—	4	1	no	—
189	C₂×C₄×C₆₁	#123	1	2	yes	—
190	C₂×C₄×C₆₁	#123	1	2	yes	—
191	C₂×C₄×C₆₁	#135	1	2	yes	—
192	C₂×C₄×C₆₁	#137	1	2	yes	—
193	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
199	C₈×C₆₁	—	4	2	no	—
200	C₈×C₆₁	—	4	1	no	—
201	C₈×C₆₁	—	4	1	no	—
202	#24972	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₆₁	—	4	2	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	2	no	—
207	C₂²×C₆₁	—	4	2	no	—
208	C₂²×C₆₁	—	4	2	no	—
209	C₂²×C₆₁	—	4	2	no	—
210	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
211	C₂²×C₆₁	#546	1	1	yes	characteristic
212	C₂²×C₆₁	#546	1	1	yes	characteristic
213	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
214	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
215	C₂²×C₆₁	#577	1	1	yes	characteristic
216	C₂²×C₆₁	#577	1	1	yes	characteristic
217	C₄×C₆₁	—	2	2	no	—
218	C₄×C₆₁	—	4	2	no	—
219	C₄×C₆₁	—	4	2	no	—
220	C₄×C₆₁	—	4	2	no	—
221	C₄×C₆₁	—	8	1	no	—
222	C₄×C₆₁	—	8	1	no	—
223	C₄×C₆₁	—	8	2	no	—
224	C₄×C₆₁	—	8	2	no	—
225	C₄×C₆₁	#485	1	4	yes	—
226	C₄×C₆₁	#529	1	1	yes	characteristic
227	C₄×C₆₁	#540	1	1	yes	characteristic
228	C₄×C₆₁	#553	1	1	yes	characteristic
229	C₄×C₆₁	#555	1	1	yes	characteristic
230	#2538	C₂×C₆₁	1	1	yes	characteristic
231	#2354	C₂×C₆₁	1	1	yes	characteristic
232	#2077	C₂×C₆₁	1	2	yes	complemented
233	#2035	C₂×C₆₁	1	2	yes	complemented
234	#1954	C₂×C₆₁	1	1	yes	characteristic
235	#1948	C₂×C₆₁	1	1	yes	characteristic, complemented
236	#1873	C₂×C₆₁	1	2	yes	complemented
237	#1834	C₂×C₆₁	1	1	yes	characteristic, complemented
238	#1825	C₂×C₆₁	1	2	yes	complemented
239	#1803	C₂×C₆₁	1	1	yes	characteristic, complemented
240	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
241	C₂×C₆₁	—	8	2	no	—
242	C₂×C₆₁	#2420	1	1	yes	characteristic
243	C₂×C₆₁	C₂×#485	1	1	yes	characteristic
244	C₂×C₆₁	#3099	1	1	yes	characteristic
245	C₂×C₆₁	#3304	1	1	yes	characteristic
246	C₂×C₆₁	#3304	1	1	yes	characteristic
247	C₂×C₆₁	#3329	1	1	yes	characteristic
248	C₂×C₆₁	#3331	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
252	C₂×#117	C₂²×C₆₁	1	2	yes	—
253	C₂×#106	C₂²×C₆₁	1	2	yes	—
254	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
257	C₂×#103	C₂²×C₆₁	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
260	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
261	#396	—	2	2	no	—
262	#390	—	2	1	no	—
263	#390	—	2	1	no	—
264	#389	—	2	1	no	—
265	#388	—	2	2	no	—
266	#384	C₂²×C₆₁	1	1	yes	characteristic
267	#384	C₂²×C₆₁	1	1	yes	characteristic
268	#380	C₂²×C₆₁	1	2	yes	—
269	#380	C₂²×C₆₁	1	2	yes	—
270	C₄×C₄⋊C₄	—	2	1	no	—
271	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
272	#340	C₂²×C₆₁	1	2	yes	—
273	#340	C₂²×C₆₁	1	1	yes	characteristic
274	#340	C₂²×C₆₁	1	2	yes	—
275	#340	C₂²×C₆₁	1	1	yes	characteristic
276	#340	C₂²×C₆₁	1	2	yes	—
277	#340	C₂²×C₆₁	1	2	yes	—
278	C₆₁	#24972	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
280	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
282	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	4	2	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	#117	—	2	4	no	—
292	#117	—	4	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
314	#106	—	4	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	#103	—	2	2	no	—
317	#103	—	2	2	no	—
318	#103	—	4	2	no	—
319	C₂²⋊C₈	—	4	2	no	—
320	C₂²⋊C₈	—	4	2	no	—
321	C₄×C₈	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	1	no	—
324	#95	—	2	2	no	—
325	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	#41×C₆₁	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	8	1	no	—
375	C₄⋊C₄	—	8	1	no	—
376	C₄⋊C₄	#41×C₆₁	1	2	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	4	4	no	—
383	C₄²	—	4	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	#41×C₆₁	1	2	yes	—
386	C₄²	#41×C₆₁	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	D₄	—	4	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	#123×C₆₁	1	2	yes	—
428	C₂×C₄	#123×C₆₁	1	2	yes	—
429	C₂×C₄	#135×C₆₁	1	2	yes	—
430	C₂×C₄	#137×C₆₁	1	2	yes	—
431	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
435	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
436	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
448	C₂²	C₆₁×#546	1	1	yes	characteristic
449	C₂²	C₆₁×#546	1	1	yes	characteristic
450	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
451	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
452	C₂²	C₆₁×#577	1	1	yes	characteristic
453	C₂²	C₆₁×#577	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	C₆₁×#485	1	4	yes	—
463	C₄	C₆₁×#529	1	1	yes	characteristic
464	C₄	C₆₁×#540	1	1	yes	characteristic
465	C₄	C₆₁×#553	1	1	yes	characteristic
466	C₄	C₆₁×#555	1	1	yes	characteristic
467	C₂	—	8	2	no	—
468	C₂	C₆₁×#2420	1	1	yes	characteristic
469	C₂	C₂×C₆₁×#485	1	1	yes	characteristic
470	C₂	C₆₁×#3099	1	1	yes	characteristic
471	C₂	C₆₁×#3304	1	1	yes	characteristic
472	C₂	C₆₁×#3304	1	1	yes	characteristic
473	C₂	C₆₁×#3329	1	1	yes	characteristic
474	C₂	C₆₁×#3331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₆₁×#2077	C₂	semidirect
4. C₆₁×#2035	C₂	semidirect
6. C₆₁×#1948	C₂	semidirect
7. C₆₁×#1873	C₂	semidirect
8. C₆₁×#1834	C₂	semidirect
9. C₆₁×#1825	C₂	semidirect
10. C₆₁×#1803	C₂	semidirect
11. C₄×#103×C₆₁	C₂	semidirect
202. #24972	C₆₁	direct (N × H)
232. #2077	C₂×C₆₁	semidirect
233. #2035	C₂×C₆₁	semidirect
235. #1948	C₂×C₆₁	semidirect
236. #1873	C₂×C₆₁	semidirect
237. #1834	C₂×C₆₁	semidirect
238. #1825	C₂×C₆₁	semidirect
239. #1803	C₂×C₆₁	semidirect
240. C₄×#103	C₂×C₆₁	semidirect
278. C₆₁	#24972	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#2538	2
C₆₁×#2354	2
C₆₁×#2077	2
C₆₁×#2035	2
C₆₁×#1954	2
C₆₁×#1948	2
C₆₁×#1873	2
C₆₁×#1834	2
C₆₁×#1825	2
C₆₁×#1803	2
C₄×#103×C₆₁	2
#24972	61

Subgroups — C61×#24972 #29528405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24972 #29528405